Reaction paths and elementary bifurcations tracks: The diabatic 1B2-state of ozone

International Journal of Bifurcation and Chaos

Volumn 16, Issue 7, 2006, Pages 1913-1928

  Farantos, S C ^a   Qu, Zheng Wang ^b   Zhu, H ^b   Schinke, R ^b  

^a INSTITUTE OF ELECTRONIC STRUCTURE AND LASER   (Greece)

^b MAX PLANCK INSTITUTE FOR DYNAMICS AND SELF ORGANIZATION   (Germany)

Author keywords

Bifurcation theory; Classical and quantum molecular dynamics; Periodic orbits

Indexed keywords

CHEMICAL BONDS; DISSOCIATION; ISOMERIZATION; NONLINEAR CONTROL SYSTEMS; OZONE; QUANTUM THEORY; SPECTROSCOPIC ANALYSIS;

BIFURCATION THEORY; CLASSICAL AND QUANTUM MOLECULAR DYNAMICS; ELEMENTARY BIFURCATIONS; PERIODIC ORBITS;

BIFURCATION (MATHEMATICS);

EID: 33748522036     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127406015799     Document Type: Article

References (65)

1. Allgower, E. L. & Georg, K. [1993] Numerical Continuation Methods, Springer Series in Computational Mathematics, Vol. 13 (Springer-Verlag, Berlin).
2. Arnold, V. I. [1980] Mathematical Methods of Classical Mechanics, Graduate Text in Mathematics, Vol. 60 (Springer-Verlag).
3. Azzam, T., Schinke, R., Farantos, S. G., Joyeux, M. & Peterson, K. A. [2003] "The bound state spectrum of HOBr up to dissociation limit: Evolution of saddle-node bifurcations," J. Chem. Phys. 118, 9643-9652.
4. Bacic, Z. & Light, J. C. [1989] "Theoretical methods for rovibrational states of floppy molecules," Ann. Rev. Phys. Chem. 40, 469-498.
5. Berry, M. V. & Tabor, M. [1977] "Calculating the bound spectrum by path summation in action-angle variables," J. Phys. A 10, 371-379.
6. Borondo, F., Zembekov, A. A. & Benito, R. M. [1996] "Saddle-node bifurcations in the LiNC/LiCN molecular system: Classical aspects and quantum manifestations," J. Chem. Phys. 105, 5068-5081.
7. Contopoulos, G., Farantos, S. C., Papadaki, H. & Polymilis, C. [1994] "Complex unstable periodic orbits and their manifestation in classical and quantum dynamics," Phys. Rev. E 50, 4399-4403.
8. Contopoulos, G., Grousouzakou, E. & Polymilis, C. [1996] "Distributions of periodic orbits and the homo-Reicheclinic tangle," Cel. Mech. Dyn. Astron. 64, 363-381.
9. Crawford, J. D. [1991] "Introduction to bifurcation theory," Rev. Mod. Phys. 63, 991-1037.
10. Crim, F. F. [1999] "Vibrational state control of bimolecular reactions: Discovering and directing the chemistry," Acc. Chem. Res. 32, 877-884.
11. Dai, H.-L. & Field, R. W. [1995] Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping (World Scientific, Singapore).
12. 2 just below the first dissociation threshold," J. Phys. Chem. 104, 10374-10382.
13. Echave, J. & Clary, D. C. [1992] "Potential optimized discrete variable representation," Chem. Phys. Lett. 190, 225-230.
14. Farantos, S. C. [1992] "Chemical dynamics: A periodic orbits approach," in Time Dependent Quantum Mechanics: Experiments and Theory, eds. Broeckhove, J. &: Lathouwers, L., NATO Advanced Science Institutes Series B: Physics, Vol. 299 (Plenum Co. Ltd), pp. 27-43.
15. Farantos, S. C. [1993] "Periodic orbits as a probe to reveal exotic states: The saddle-node states," Laser Chem. 13, 87-99.
16. Farantos, S. C. [1996] "Exploring molecular vibrations with periodic orbits," Int. Rev. Phys. Chem. 15, 345-374.
17. Farantos, S. C. [1998] "POMULT: A program for computing periodic orbits in Hamiltonian systems based on multiple shooting algorithms," Comp. Phys. Comm. 108, 240-258.
18. 1)," Chem. Phys. Lett. 399, 260-265.
19. Flach, S. & Willis, C. R. [1998] "Discrete breathers," Phys. Rep. 295, 181-264.
20. 2," Chem. Phys. Lett. 277, 456-464.
21. Grozdanov, T. P., Mandelshtam, V. A. & Taylor, H. S. [1995] "Recursion polynomial expansion of the Green's function with absorbing boundary conditions: Calculations of resonances of HCO by filter diagonalization," J. Chem. Phys. 103, 7990-7995.
22. 3," J. Chem. Phys. 111, 10836-10842.
23. Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (Springer-Verlag, Berlin).
24. Gutzwiller, M. C. [1990] Chaos in Classical and Quantum Mechanics, Vol. 1 (Springer-Verlag).
25. Halonen, L. [1998] "Local mode vibrations in polyatomic molecules," Adv. Chem. Phys. 104, 41-179.
26. Heller, E. J. [1984] "Bound-state eigenfunctions of classically chaotic Hamiltonian systems: Scars of periodic orbits," Phys. Rev. Lett. 53, 1515-1518.
27. Herman, M., Lievin, J. & Auwera, J. V. [1999] "Global and accurate vibration Hamiltonians from high-resolution molecular spectroscopy," Adv. Chem. Phys. Vol. 108 (John Wiley and Sons, Inc.), pp. 1-431.
28. Houston, P. L. [2003] "Photodissociation dynamics of ozone in the Hartley band," in Modern Trends in Chemical Dynamics, eds. Yang, X. & Liu, K., Advanced Series in Physical Chemistry, Vol. 14 (World Scientific, Singapore), p. 197.
29. Ishikawa, H., Nagao, C., Mikami, N. & Field, R. W. [1998] "Spectroscopic investigation of the generation of 'isomerization' states: Eigenvector analysis of the bend-CP stretch polyad," J. Chem. Phys. 109, 492-503.
30. Ishikawa, H., Field, R. W., Farantos, S. C., Joyeux, M., Koput, J., Beck, C. & Schinke, R. [1999] "HCP ↔ CPH isomerization: Caught in the act," Ann. Rev. Phys. Chem. 50, 443-484.
31. -1 of internal energy," J. Chem. Phys. 109, 3831-3840.
32. -1 of internal energy," J. Chem. Phys. 109, 121-133.
33. Jacobson, M. P., Silbey, R. J. & Field, R. W. [1999] "Local mode behavior in the acetylene bending system," J. Chem. Phys. 110, 845-859.
34. Jonas, D. M., Solina, S. A. B., Rajaram, B., Silbey, R. J., Field, R. W., Yamanouchi, K. & Tsuchiya, S. [1993] "Intramolecular vibrational redistribution of energy in the stimulated emission pumping spectrum of acetylene," J. Chem. Phys. 99, 7350-7370.
35. Joyeux, M., Farantos, S. C. & Schinke, R. [2002] "Highly excited motion in molecules: Saddle-node bifurcations and their fingerprints in vibrational spectra," J. Phys. Chem. 106, 5407-5421.
36. Joyeux, M., Grebenshchikov, S. Yu, Bredenbeck, J., Schinke, R. & Farantos, S. C. [2005] "Intramolecular dynamics along isomerization and dissociation pathways," in Geometrical Structures of Phase Space in Multi-Dimensional Chaos, Adv. Chem. Phys. Vol. 130, pp. 267-303.
37. Keller, H.-M., Flöthmann, H.-M., Dobbyn, A. J., Schinke, R., Werner, H.-J., Bauer, C. & Rosmus, P. [1996] "The unimolecular dissociation of HCO. II. Comparison of calculated resonance energies and widths with high-resolution spectroscopic data," J. Chem. Phys. 105, 4983-5004.
38. 2 A). II. Calculation of resonance energies and widths and comparison with high-resolution spectroscopic data," J. Chem. Phys. 106, 5359-5378.
39. Kopidakis, G. & Aubry, S. [1999] "Intraband discrete breathers in disordered nonlinear systems. I. Delocalization," Physica D 130, 155-309.
40. 2O classical and semiclassical considerations," Mol. Phys. 44, 709-723.
41. Light, J. C. & Carrington, T. [2000] "Discrete-variable representations and their utilization," Adv. Chem. Phys. 114, 263-310.
42. 1) and their roles in unimolecular and bimolecular reactions," J. Chem. Phys. 122, 124308.
43. Mandelshtam, V. A. & Taylor, H. S. [1997] "A lowstorage filter diagonalization method for quantum eigenergy calculations or for spectral analysis of time signals," J. Chem. Phys. 106, 5085-5090.
44. Moser, J. [1976] "Periodic orbits near an equilibrium and a theorem by Alan Weinstein," Commun. Pure Appl. Math. 29, 727-747.
45. Newhouse, S. E. [1979] "The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms," Publ. Math. IHES 50, 101-151.
46. Northrup, F. J., Bethardy, G. A. & Macdonald, R. G. [1997] "Infrared absorption spectroscopy of HNC in the region 2.6 to 3.1 μm," J. Mol. Spectrosc. 186, 349-362.
47. Ozorio de Almeida, A. M. [1990] Hamiltonian Systems: Chaos and Quantization (Cambridge University Press, NY).
48. 2 system," J. Chem. Phys. 103, 3299-3314.
49. 2 by periodic orbits," Chem. Phys. Lett. 311, 241-247.
50. Prosmiti, R. & Farantos, S. C. [2003] "Periodic orbits and bifurcation diagrams of acetylene/vinylidene revisited," J. Chem. Phys. 118, 8275-8280.
51. Qu, Z. W., Zhu, Schinke, R. & Farantos, S. C. [2004a] "The Huggins band of ozone: A theoretical analysis," J. Chem. Phys. 121, 11731-11745.
52. Qu, Z. W., Zhu, H., Tashiro, M., Schinke, R. & Farantos, S. C. [2004b] "The Huggins band of ozone: Unambiguous electronic and vibrational assignment," J. Chem. Phys. 120, 6811-6814.
53. 2. Vibrational wavefunctions from spectroscopy," Chem. Phys. Lett. 264, 403-410.
54. Stamatiadis, S., Prosmiti, R. & Farantos, S. C. [2000] "AUTO_DERIV: Tool for automatic differentiation of a FORTRAN code," Comp. Phys. Comm. 127, 343-355.
55. van der Meer, J.-C. [1985] The Hamiltonian Hopf Bifurcation, Vol. 1160 (Springer-Verlag, NY).
56. Wall, M. R. & Neuhauser, D. [1995] "Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. I. Theory and application to a quantum-dynamics model," J. Chem. Phys. 102, 8011-8022.
57. Weinstein, A. [1973] "Normal modes for nonlinear Hamiltonian systems," Inv. Math. 20, 47-57.
58. Weish, J., Hauschildt, J., Düren, R., Schinke, R., Koput, J., Stamatiadis, S. & Farantos, S. C. [2000] "Saddle-node bifurcations and their quantum mechanical fingerprints in the spectrum of HOCl," J. Chem. Phys. 112, 77-93.
59. Wiggins, S. [2003] Introduction to Applied Nonlinear Dynamical Systems and Chaos, Second Edition (Springer-Verlag, NY).
60. Xie, A., van der Meer, L., Hoff, W. & Austin, R. H. [2000] "Long-lived amide I vibrational modes in myoglobin," Phys. Rev. Lett. 84, 5435-5438.
61. Yakubovich, V. A. & Starzhinskii, V. M. [1975] Linear Differential Equations with Periodic Coefficients, Vol. 1 (Halsted Press).
62. Yamamoto, T. & Kato, S. [1998] "Quantum dynamics of unimolecular dissociation reaction HFCO → HF + CO," J. Chem. Phys. 109, 9783-9794.
63. 2 in the electronic ground state as studied by stimulated emission pumping spectroscopy," J. Chem. Phys. 88, 4664-4670.
64. 2 in the electronic ground state. II. Vibrational assignment by dispersed fluorescence and stimulated emission pumping spectroscopy," J. Chem. Phys. 92, 4044-4054.
65. Zou, S. & Bowman, J. M. [2002] "Full dimensionality quantum calculations of acetylene/vinylidene isomerization," J. Chem. Phys. 117, 5507-5510.